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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Square root, Representation and Logarithm of complex numbers

  • question_answer
    If \[{{e}^{i\theta }}=\cos \theta +i\sin \theta \], then in \[\Delta ABC\] value of \[{{e}^{iA}}.{{e}^{iB}}.{{e}^{iC}}\]  is  [AMU 2005]

    A) -i

    B) 1

    C) -1

    D) None of these

    Correct Answer: C

    Solution :

    \[{{e}^{iA}}.{{e}^{iB}}.{{e}^{iC}}={{e}^{iA+iB+iC}}={{e}^{i(A+B+C)}}={{e}^{i\pi }}\] [\[\therefore \,A+B+C=\pi \]] = \[\cos \pi +i\sin \pi =(-1)+i(0)=-1\].


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